
theorem
  7549 is prime
proof
  now
    7549 = 2*3774 + 1; hence not 2 divides 7549 by NAT_4:9;
    7549 = 3*2516 + 1; hence not 3 divides 7549 by NAT_4:9;
    7549 = 5*1509 + 4; hence not 5 divides 7549 by NAT_4:9;
    7549 = 7*1078 + 3; hence not 7 divides 7549 by NAT_4:9;
    7549 = 11*686 + 3; hence not 11 divides 7549 by NAT_4:9;
    7549 = 13*580 + 9; hence not 13 divides 7549 by NAT_4:9;
    7549 = 17*444 + 1; hence not 17 divides 7549 by NAT_4:9;
    7549 = 19*397 + 6; hence not 19 divides 7549 by NAT_4:9;
    7549 = 23*328 + 5; hence not 23 divides 7549 by NAT_4:9;
    7549 = 29*260 + 9; hence not 29 divides 7549 by NAT_4:9;
    7549 = 31*243 + 16; hence not 31 divides 7549 by NAT_4:9;
    7549 = 37*204 + 1; hence not 37 divides 7549 by NAT_4:9;
    7549 = 41*184 + 5; hence not 41 divides 7549 by NAT_4:9;
    7549 = 43*175 + 24; hence not 43 divides 7549 by NAT_4:9;
    7549 = 47*160 + 29; hence not 47 divides 7549 by NAT_4:9;
    7549 = 53*142 + 23; hence not 53 divides 7549 by NAT_4:9;
    7549 = 59*127 + 56; hence not 59 divides 7549 by NAT_4:9;
    7549 = 61*123 + 46; hence not 61 divides 7549 by NAT_4:9;
    7549 = 67*112 + 45; hence not 67 divides 7549 by NAT_4:9;
    7549 = 71*106 + 23; hence not 71 divides 7549 by NAT_4:9;
    7549 = 73*103 + 30; hence not 73 divides 7549 by NAT_4:9;
    7549 = 79*95 + 44; hence not 79 divides 7549 by NAT_4:9;
    7549 = 83*90 + 79; hence not 83 divides 7549 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7549 & n is prime
  holds not n divides 7549 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
